Problems 8201 to 8300

Table 2.167: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

8201	$[\begin{matrix} x^{'} = 3 x + 2 y \\ y^{'} = - 2 x - y \end{matrix}]$	system_of_ODEs	✓	0.368

8202	$[\begin{matrix} x^{'} = x + y \\ y^{'} = - x + y \end{matrix}]$	system_of_ODEs	✓	0.367

8203	$[\begin{matrix} x^{'} = 3 x - 5 y \\ y^{'} = - x + 2 y \end{matrix}]$	system_of_ODEs	✓	0.609

8204	$[\begin{matrix} x^{'} = x + 2 y \\ y^{'} = - 4 x + y \end{matrix}]$	system_of_ODEs	✓	0.515

8205	$[\begin{matrix} x^{'} = 3 x + 2 y + z \\ y^{'} = - 2 x - y + 3 z \\ z^{'} = x + y + z \end{matrix}]$	system_of_ODEs	✓	0.637

8206	$[\begin{matrix} x^{'} = - x + y - z \\ y^{'} = 2 x - y - 4 z \\ z^{'} = 3 x - y + z \end{matrix}]$	system_of_ODEs	✓	9.538

8207	$[\begin{matrix} x^{'} = x + 2 y - 4 t + 1 \\ y^{'} = - x + 2 y + 3 t + 4 \end{matrix}]$	system_of_ODEs	✓	1.453

8208	$[\begin{matrix} x^{'} = - 2 x + y - t + 3 \\ y^{'} = x + 4 y + t - 2 \end{matrix}]$	system_of_ODEs	✓	2.022

8209	$[\begin{matrix} x^{'} = - 4 x + y - t + 3 \\ y^{'} = - x - 5 y + t + 1 \end{matrix}]$	system_of_ODEs	✓	1.373

8210	$[\begin{matrix} x^{'} = x y + 1 \\ y^{'} = - x + y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.061

8211	$[\begin{matrix} x^{'} = 1 + t y \\ y^{'} = - t x + y \end{matrix}]$ i.c.	system_of_ODEs	✓	0.062

8212	$y^{'} = - x + y^{2}$ i.c.	[[_Riccati, _special]]	✓	0.301

8213	$y^{'} = - x + y^{2}$ i.c.	[[_Riccati, _special]]	✓	2.088

8214	$y^{'} - 2 y = x^{2}$ i.c.	[[_linear, ‘class A‘]]	✓	0.488

8215	$y^{'} - 2 y = x^{2}$ i.c.	[[_linear, ‘class A‘]]	✓	1.262

8216	$y^{'} = y + x e^{y}$ i.c.	[‘y=_G(x,y’)‘]	✓	0.976

8217	$y^{'} = y + x e^{y}$ i.c.	[‘y=_G(x,y’)‘]	✗	1.251

8218	$y^{''} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.358

8219	$y^{''} + y = 0$	[[_2nd_order, _missing_x]]	✓	1.372

8220	$y^{''} - y = 0$	[[_2nd_order, _missing_x]]	✓	0.342

8221	$y^{''} - y = 0$	[[_2nd_order, _missing_x]]	✓	1.511

8222	$y^{''} - y^{'} = 0$	[[_2nd_order, _missing_x]]	✓	0.386

8223	$y^{''} - y^{'} = 0$	[[_2nd_order, _missing_x]]	✓	0.795

8224	$y^{''} + 2 y^{'} = 0$	[[_2nd_order, _missing_x]]	✓	0.397

8225	$y^{''} + 2 y^{'} = 0$	[[_2nd_order, _missing_x]]	✓	1.101

8226	$y^{''} - x y = 0$	[[_Emden, _Fowler]]	✓	0.327

8227	$y^{''} + x^{2} y = 0$	[[_Emden, _Fowler]]	✓	0.407

8228	$y^{''} - 2 y^{'} x + y = 0$	[_Lienard]	✓	0.428

8229	$y^{''} - y^{'} x + 2 y = 0$	[_Hermite]	✓	0.449

8230	$y^{''} + x^{2} y^{'} + x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.443

8231	$y^{''} + 2 y^{'} x + 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.469

8232	$(x - 1) y^{''} + y^{'} = 0$	[[_2nd_order, _missing_y]]	✓	0.455

8233	$(x + 2) y^{''} + y^{'} x - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.462

8234	$y^{''} - (x + 1) y^{'} - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.551

8235	$(x^{2} + 1) y^{''} - 6 y = 0$	[[_Emden, _Fowler]]	✓	0.479

8236	$(x^{2} + 2) y^{''} + 3 y^{'} x - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.579

8237	$(x^{2} - 1) y^{''} + y^{'} x - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.487

8238	$(x - 1) y^{''} - y^{'} x + y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.454

8239	$(x + 1) y^{''} - (2 - x) y^{'} + y = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.622

8240	$y^{''} - 2 y^{'} x + 8 y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.512

8241	$(x^{2} + 1) y^{''} + 2 y^{'} x = 0$ i.c.	[[_2nd_order, _missing_y]]	✓	0.515

8242	$y^{''} + y \sin (x) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.750

8243	$y^{''} + e^{x} y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.850

8244	$\cos (x) y^{''} + y^{'} + 5 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	2.949

8245	$\cos (x) y^{''} + y^{'} + 5 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	6.839

8246	$y^{''} - x y = 1$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.350

8247	$y^{''} - 4 y^{'} x - 4 y = e^{x}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	0.583

8248	$x y^{''} + y \sin (x) = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.926

8249	$y^{''} + 5 y^{'} x + y \sqrt{x} = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.214

8250	$y^{''} + y^{'} x + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.482

8251	$y^{''} + \cos (x) y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	0.793

8252	$x^{3} y^{''} + 4 x^{2} y^{'} + 3 y = 0$	[[_Emden, _Fowler]]	✗	0.171

8253	$x {(3 + x)}^{2} y^{''} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.524

8254	${(x^{2} - 9)}^{2} y^{''} + (3 + x) y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.765

8255	$y^{''} - \frac{y^{'}}{x} + \frac{y}{{(x - 1)}^{3}} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.786

8256	$(x^{3} + 4 x) y^{''} - 2 y^{'} x + 6 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.696

8257	$x^{2} {(x - 5)}^{2} y^{''} + 4 y^{'} x + (x^{2} - 25) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.619

8258	$(x^{2} + x - 6) y^{''} + (3 + x) y^{'} + (x - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.673

8259	$x {(x^{2} + 1)}^{2} y^{''} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.493

8260	$x^{3} (x^{2} - 25) {(x - 2)}^{2} y^{''} + 3 x (x - 2) y^{'} + 7 (5 + x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	0.195

8261	${(x^{3} - 2 x^{2} + 3 x)}^{2} y^{''} + x {(x - 3)}^{2} y^{'} - (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.293

8262	$(x^{2} - 1) y^{''} + 5 (x + 1) y^{'} + (x^{2} - x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.773

8263	$x y^{''} + (3 + x) y^{'} + 7 x^{2} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.568

8264	$x^{2} y^{''} + (\frac{5}{3} x + x^{2}) y^{'} - \frac{y}{3} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.928

8265	$x y^{''} + y^{'} + 10 y = 0$	[[_Emden, _Fowler]]	✓	0.678

8266	$2 x y^{''} - y^{'} + 2 y = 0$	[[_Emden, _Fowler]]	✓	0.934

8267	$2 x y^{''} + 5 y^{'} + x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.730

8268	$4 x y^{''} + \frac{y^{'}}{2} + y = 0$	[[_Emden, _Fowler]]	✓	0.915

8269	$2 x^{2} y^{''} - y^{'} x + (x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.822

8270	$3 x y^{''} + (2 - x) y^{'} - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.816

8271	$x^{2} y^{''} - (x - \frac{2}{9}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.979

8272	$2 x y^{''} - (2 x + 3) y^{'} + y = 0$	[_Laguerre]	✓	0.871

8273	$x^{2} y^{''} + y^{'} x + (x^{2} - \frac{4}{9}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.767

8274	$9 x^{2} y^{''} + 9 x^{2} y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.020

8275	$2 x^{2} y^{''} + 3 y^{'} x + (2 x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.907

8276	$x y^{''} + 2 y^{'} - x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.729

8277	$x^{2} y^{''} + y^{'} x + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.798

8278	$x y^{''} - y^{'} x + y = 0$	[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.446

8279	$y^{''} + \frac{3 y^{'}}{x} - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.254

8280	$x y^{''} + (1 - x) y^{'} - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.656

8281	$x y^{''} + y^{'} + y = 0$	[[_Emden, _Fowler]]	✓	0.657

8282	$x y^{''} + (x - 6) y^{'} - 3 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.943

8283	$x (x - 1) y^{''} + 3 y^{'} - 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.802

8284	$y^{''} + \frac{2 y^{'}}{t} + λ y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.771

8285	$x^{3} y^{''} + y = 0$	[[_Emden, _Fowler]]	✗	0.149

8286	$x^{2} y^{''} + (3 x - 1) y^{'} + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✗	0.214

8287	$x^{2} y^{''} + y^{'} x + (x^{2} - \frac{1}{9}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.504

8288	$x^{2} y^{''} + y^{'} x + (x^{2} - 1) y = 0$	[_Bessel]	✓	0.559

8289	$4 x^{2} y^{''} + 4 y^{'} x + (4 x^{2} - 25) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.702

8290	$16 x^{2} y^{''} + 16 y^{'} x + (16 x^{2} - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.579

8291	$x y^{''} + y^{'} + x y = 0$	[_Lienard]	✓	0.508

8292	$x y^{''} + y^{'} + (x - \frac{4}{x}) y = 0$	[_Bessel]	✓	0.569

8293	$x^{2} y^{''} + y^{'} x + (9 x^{2} - 4) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.586

8294	$x^{2} y^{''} + y^{'} x + (36 x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.662

8295	$x^{2} y^{''} + y^{'} x + (25 x^{2} - \frac{4}{9}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.540

8296	$x^{2} y^{''} + y^{'} x + (2 x^{2} - 64) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.663

8297	$x y^{''} + 2 y^{'} + 4 y = 0$	[[_Emden, _Fowler]]	✓	0.331

8298	$x y^{''} + 3 y^{'} + x y = 0$	[_Lienard]	✓	0.505

8299	$x y^{''} - y^{'} + x y = 0$	[_Lienard]	✓	0.508

8300	$x y^{''} - 5 y^{'} + x y = 0$	[_Lienard]	✓	0.545

2.2.83 Problems 8201 to 8300